Firefighters fought the blaze in the upper floors of the Brandon Court high rise block at around 12pm on Thursday.
The fire started after a chip pan cooker was accidentally switched, the fire service said.
A large amount of smoke filled the kitchen and a man and a woman suffered smoke inhalation as a result.
They were taken to Wishaw General Hospital for precautionary check-ups.
Watch Manager Robert McNaughton, the incident commander, said: "A small fire in a chip pan had caused a large amount of smoke to fill the kitchen.
"Firefighters in breathing apparatus quickly put out the flames using a dry powder extinguisher and our crews provided oxygen therapy to two people who had suffered smoke inhalation.
"This fire started when a chip pan on the cooker was accidentally switched on.
"It shows how easily a fire can start and why we all need to take action to reduce the risk to ourselves and those around us.
"We know even a moment's distraction can see a fire start in the kitchen and small fires still produce thick smoke that threatens lives and can cause significant damage to property.
"Thankfully this home was protected by a working smoke alarm and the residents had the presence to mind to get out, closing the kitchen door behind them as they left, and call us out."